I agree, patch is fairly satisfying result but I suspect the down side is the reverse in curvature approaching the corners.
Here’s a maybe too-complicated way - with Loose loft. With straights and true arcs on the corners, (i.e. G1 only) a really nice bubble is tricky, it seems to me.
Hi Michael - subD might be OK but you will not get the full arc shape - it will flatten out as it approaches the edges. Also, if you can compromise the arcs on the corners, there is more you can do with surfaces as well, I would say - that is, make the corners G2 to the sides.